Exercise 2. The transform associated uwrith a random variable Y has the form Y(s)a Find a, py(41)...
Problem1 Random variable Y has a probability mass function (pmf) as py(y) = a) Find the value of the constant c ,y=1,2,3 , y =-1,-2,-3 0 otherwise b) Now that the constant c is determined, find (G) Probability of Y 1 (ii) Probability of Y<1
Exercise 3. The transforms associated with two independent discrete random variables X and Y are S(e-1) P(X + Y = 15). Justify your answer. Find
between zero and one. Find the PDF of X+Y+Z 5. Let X be a random variable that takes nonnegative integer values, and is associated with a transform of the form 3- es where c is some scalar. Find EX], px (1), and E(XX # 0]
between zero and one. Find the PDF of X+Y+Z 5. Let X be a random variable that takes nonnegative integer values, and is associated with a transform of the form 3- es where c is...
Exercise 7. Let X and Y be A. independent exponential random variables with a common parameter (1) Find the transform associated with aX +Y, where a is a constant. (2) Use the result of part (1) to find the PDF of aX +Y, for the case where a is positive and different than1 (3) Use the result of part (1) to find the PDF of X-Y. Justify your answers.
Exercise 7. Let X and Y be A. independent exponential random...
7. A positive random variable Y is said to be a lognormal random variable, LOGN (u, 0), if In Y ~ N(No?). We assume that Y, LOGN (1,0%), i = 1,..., n are independent. [5] (a) Find the distribution of T = 11",Y. [4] (b) Find E(T) and Var(T) (5] (c) If we assume that M = ... = Hn and a = ... = 0, what does the the successive geometric average, lim (II",Y), converge in probability to? Justify...
Exercise 1. Let X be a random variable such that Find a, b, and c, and the PMF of X. Justify your answer
Exercise 1. Let X be a random variable such that Find a, b, and c, and the PMF of X. Justify your answer
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
1. (a) Consider the random variable Y having possible values 1, 2 and 3. The corresponding probability for each value is: 1 with probability Y = 2 with probability 3 with probability Determine an expression for the probability mass function (pmf) (11) Determine the mean and the standard deviation of Y. (b) The probability that a man hits a target is and that of his son and daughter are and respectively. If they all fire together, find the probability that:...
2. The random variable of Y has the following distribution function for y<2 for 2 sy < 2.5 for 2.5 s y<4 for 4 sy< 5.5 for 5.5 S y<6 for 6 sy7 for y 2 1.0 F(Y) Find the probability distribution of Y. We were unable to transcribe this image
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Find the CDF of Y (c) Find E[Y] and Var(Y] (d) Find P IYel Y 3]
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| |...